We booked a United flight (operated by Lufthansa) from Washington, DC to Istanbul with a 3.5 hour layover in Frankfurt but just received notice that a new departure time will only allow a 1 hour layover, a connection that will be impossible to make. There are 3 flights leaving Frankfurt later in the day for Istanbul. We are trying to decide whether to trust our luck that we can be rebooked onto one of these flights, or deposit the money we paid for the flight into our account and book a direct flight on Turkish Airlines with points.

What do you say it is an impossible connection? MCT at FRA used to be 45 minutes but this year that was changed to 60 minutes - so it is a totally legal connection. Since you are flying non-Schengen to non-Schengen you won't go through Immigration or Customs.

I would check the later flights to see seat availability FRA-IST if you are flying soon and check if your dates fall on some holiday period.
if everything looks good I would keep your original flights. Might have a sl higher chance of losing your luggage if you checked with a one hour connection but if you are staying in Istanbul they will most likely get your bags to you next day. Luggage delay insurance may be an idea too if checking bags

I will go against the grain. Speaking as the Queen of Delayed Luggage (12 incidents) I would rebook to one of the later flights from FRA. But that's just me, being very risk-averse.

Seems you have done your homework and just need to make a decision. If you can switch to a longer connection, of course your chances of running issues is lower.

I will say this but I was going the opposite direction twice. I just barely got to my gate as the flight was just boarding. My checked luggage made it as did I but I was so frantic. I wouldn't even use the bathroom before boarding the connecting flight (connection went from 1 hr 50 minutes to about an hour due to being delayed). I had the same in Oslo so different airport with 50 minutes but oh my heart and I desperately needed to get home. Both were not something I would have gladly agreed to if I had another choice.

So if it doesn't cost extra and you are ok with another flight, i would change it.

My post should have said "Why do you say it is an impossible connection? . . ."

To clarify -- IF my final destination was in Schengen I would not like a 1 hour connection. But since you are merely transiting and not entering Schengen you won't have to deal with Immigration, Customs or security.

Sassy makes a good point about the stress of a short layover. Travel is stressful enough, who needs more? That's another reason to rebook.

I may be wrong, but I do believe immigration IS checked at your first arrival point into Schengen area...

AFAIK non-Shengen to non-Schengen single ticket itineraries are merely in transit and do not go through Shengen Border Control/Immigration. They are not 'entering' Schengen so no passport control. Travelers stay airside and can go directly to the departure gate.

I've always used FRA as an entrypoint into Schengen, and I blanked on the final destination being Istanbul. 100% agree with you.. no immigration or security in this case.

My own experience at FRA (all including immigration) has been that I've made 1hr connections, and missed 3 hr scheduled connections. The latter due to factors outside my control, namely a late arriving incoming flight. Eastbound transatlantic flights often have the benefit of a tailwind, which can give you a few more minutes on the ground. I have found that Lufthansa ground agents want you to make the connecting flight, and have the ability to radio ahead to you departure gate and let them know you are on your way. So my 2 pieces of advice are:

1. be sure to make human contact with the 1st possible Lufthansa agent, who will likely be standing at the end of the jet bridge helping direct passengers to the right place... If you connection is super tight due to a late arriving plane, ask them how they can help you.

2. Have the lufthansa app on your phone, and know your rebooking options in the event that you miss your connection. Even knowing the status of your ongoing flight is good info...

Legal connection time does not mean practical connection time. Check the on time arrival record of your first leg flight to help in your decision. Personally I would opt for a later second leg if that is an option.